For analyzing movement of a continuum to investigate a fluid such as water or air by the use of a numerical calculation, that is, fluid analysis, there has been conventionally proposed a technique called particle method. Specifically, the particle method is intended to analyze motion of a continuum as motion of a finite number of particles. The currently proposed typical particle methods include SPH (smoothed particles hydrodynamics) method and MPS (moving particles semi-implicit) method. In the following description, a type of fluid such as water or air may be called “continuum” (for example, see J. J. Monaghan, “Smoothed Particle Hydrodynamics,” Annu. Rev. Astron. Astrophys., Vol. 30, pp. 543 to 574).
In the particle methods, there has been conventionally known a standard approach by which a region for a subject particle (hereinafter, called “influence domain”) is preset and interaction between the subject particle and only a counterpart particle existing in the influence domain is calculated to determine a force applied to the subject particle.
Expressing a continuum using the SPH method is characterized by smoothing and approximating physical quantities of a plurality of particles by the use of a weighting function called kernel function to discretize a basic equation. The smoothing process eliminates the need for performing extremely complicated calculations in mesh operation by which the physical quantities are evaluated on mesh points. Thus, the SPH method can be said to be suitable for dealing with free surface problems and multi-physics problems. Specifically, the SPH method can be said to be suitable for estimating the flow rate and impact pressure of sea waves colliding and overtopping shore protections, for example.
However, performing wide-range calculations by the SPH method results in a too large calculation amount. Thus, when the SPH method is used, calculations are to be performed only in a limited region of several km square at a maximum. Accordingly, with regard to propagation of tsunami waves, it is difficult to handle, by the SPH method, a process of propagation of sea waves from a source of tsunami located immediately on an earthquake center over several hundred km or more to be used in a tsunami calculation.
In addition, there is a conventional technique for conducting simulation of a fluid with a combination of topographic data and structural data (for example, see Japanese Laid-open Patent Publication No. 2005-115701). However, it is also difficult to handle, by this method, a wide range of several hundred km.
Meanwhile, there have been suggested conventional techniques for calculating a process of a tsunami from crustal deformation due to an earthquake through occurrence of a tsunami to the propagation of the tsunami from the earthquake center to the seashore by a two-dimensional propagation simulator (for example, see Japanese Laid-open Patent Publication No. 2008-089316 and Japanese Laid-open Patent Publication No. 2010-054460 and Goto, C., Ogawa, Y., Shuto, N., and Imamura, F.: Numerical method of tsunami simulation with the leap-frog scheme (IUGG/IOC Time Project), IOC Manual, UNESCO, No. 35, 1997, pp. 6 to 16). In the foregoing methods, information such as a wave height and a speed is set at each of points on a two-dimensional map, and it is possible to predict the wave height on the coast, flooded areas, and the like at occurrence of a tsunami.
There have been also proposed conventional techniques by which results of calculations in a lower dimension are given as initial conditions and boundary conditions for calculations in a higher dimension. For example, in one of the conventional techniques, an applied earthquake center and a vibration-receiving structure are treated by a three-dimensional finite element method, and vibrations transferred from the earthquake center to the structure through the ground are determined in a simplified model (for example, see Japanese Laid-open Patent Publication No. 2004-219237). In another conventional technique, a one-dimensional Boussinesq wave model and two-dimensional SPH method calculations are combined (for example, see Kassiotis et al., “Coupling SPH with a 1-D Boussinesq-type wave model”. In the conventional technique in which a one-dimensional Boussinesq wave model and two-dimensional SPH method calculations are combined, a process is performed as described below, for example. Specifically, a buffer region is set as a region in which a region for performing calculations by the SPH method and a region for performing calculations by the Boussinesq method are overlapped; in the buffer region, a speed obtained as a result of the calculations by the Boussinesq method is forcedly set to each of particles treated by the SPH method; and outside the buffer region, the speed is updated according to an acceleration obtained by solving a fluid equation of motion. However, the buffer region is predetermined and SPH particles are not generated or eliminated.
However, the conventional technique using only two-dimensional simulation have problems, in which it is difficult to handle complicated landforms in port areas and the like for which three-dimensional characteristics are important, and in which it is difficult to calculate wave pressure and wave power applied to architectural structures.
In addition, the conventional technique, by which an applied earthquake center and a vibration-receiving structure are treated by a three-dimensional finite element method and vibrations transferred from the earthquake center to the structure through the ground are determined in a simplified model, is to be applied to vibrations through the ground and thus is difficult to be used for tsunami simulation.
Further, in the conventional technique by which a Boussinesq wave model is used for calculations by the SPH method, in the case where a large amount of fluid moves as in a tsunami, when the buffer region is narrow, all of the particles in the buffer region moves to the SPH region. Consequently, calculations in the buffer region may be disabled. On the other hand, when the width of the buffer region is decided taking into account of the movement of a fluid in a tsunami, the buffer region becomes too large to be actually processed, with an extreme increase in the calculation amount and memory amount thus caused. Moreover, the conventional technique is intended for a combination of one dimension and two dimensions, not a combination of two dimensions and three dimensions, and thus is difficult to be used for calculations of tsunami propagation.